Tartarus

Hesiod measures it. A bronze anvil falling from heaven would take nine days to reach the earth, and nine more falling from earth to reach Tartarus. It is not simply a deeper basement; it is a second full drop, walled in bronze with a neck of iron, and Night is wrapped around its throat in three rows.

It is both a place and a primordial being — one of the first entities to exist alongside Chaos and Gaia, which means the prison is older than anything imprisoned in it. That detail matters: Tartarus is not built for the Titans, it precedes them.

The Titans went in after their defeat, with the Hundred-Handed Ones set as guards. So did Typhon, under Etna in some versions and in Tartarus in others. And so did the individually damned, the ones whose punishments became proverbs: Sisyphus rolling his stone, Tantalus with water receding from his lips, Ixion on a burning wheel, the Danaids filling a jar that will not hold water.

The punishments share a design. Each is endless, each is almost complete, and each fails at the last moment forever. Greek damnation is not fire; it is futility.

The Hundred-Handed Ones are the detail that makes the prison work. Freed by Zeus during the war and unbeatable in it, they were posted at the gates afterwards as guards, which means the Titans are held by beings who were themselves imprisoned by a Titan. Greek myth is fond of that shape — the jailer who used to be the prisoner.